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Consider the function ln(x + 1) and do the following.
a. Find the MacLaurin series expansion for n = 4
b. Plot ln(x + 1) and its series expansion using your graphing calculator with a window of [0, 3] X [0, 1] with Yscl = .1.
c. We use series to approximate values of functions. Therefore it is important that we know for which values of x the series will provide good approximations of the given function. Based on the graph can we use the MacLaurin series expansion to approximate ln(x + 1) for any value of x or is there a limit to the values of x? If there is a limit then what interval provides the x - values for which the MacLaurin series expansion will provide a good estimate of the value of ln(x + 1)? Explain.
d. What effect does increasing the number of terms in the series expansion have on the way it approximates the given function? Why?
Discrete sequence plot in Matlab, Consider the following formula, x[n] = x[n-1] + x[n-3] n>=3, find the rest of the sequence for 0
A voltage divder is required to produce a 5.5V output from 12V source. If one of the resistor values is 1.0k, what value is required for the second resistor so that the voltage across the 1.0k resistor is 5.5V
Show that for wires of identical dimensions but made of different materials, such as copper and aluminum, the resistance is proportional to the resistivity of the material. the resistance of a certain copper wire is 1.5.
You are planning to buy a $250,000 house and will take out a mortgage for 80% of the homes value. The term of your mortgage is 15 years and the interest rate is 4%, compounded monthly.
A "shift and add" multiplier works as follows: given two n bit numbers X and Y , look at the LSB of X: if it is one, then add Y to the running sum. If it is zero, then don't do anything (since multiplying by 0 is 0!). Next, shift X to the right by..
Starting from rest, a 4.70-kg block slides 2.10 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is k = 0.436. (a) Determine the work done by the force of gravity.
If someone presses the 1 or First floor button, the elevator should go to the 1st floor, open the door and remain in this state for a small amount of time, then close the door. Assume the elevator takes one clock cycle to travel.
For the LCD configured in 8-bit mode, describe the signal conditions for CSB, E, RS, R/W~, and the data bits (D7 thru D0) needed to write the letter character ‘A' from the microcontroller into the LCD module.
A three-phase, 318.75-kVA, 2300-V alternator has an armature resistance of 0.35 /phase and a synchronous reactance of 1.2 /phase. Determine the no-load line-to-line generated voltage and the voltage regulation
The highest frequency contained in a certain analog signal is 4 kHz. Determine the sampling rate if it is chosen to be 50% greater than the theoretical minimum.
The tray heats up according to ut = c2?u + h(x, y) where h(x, y) = 5(1 - sin(8πy)) and c2 = 10-4. Assume that u = 200 along each edge. Find the steady state temperature distribution of the tray.
A positron (same mass as electron) moving at .8c collides head on with a stationary electron producing two photons with EQUAL ANGLES relative to the incoming positron. Find the photon energies, wavelengths and angle
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